The goal of the present work was to identify and implement modifications to a density-based unstructured RANS CFD algorithm, as typically used in turbomachinery flows (represented here via the RoIIs-Royce 'Hydra' code), for application to Iow Mach number gas-turbine combustor flows. The basic algorithm was modified to make it suitable for combustor relevant problems. Fixed velocity and centreline boundary conditions were added using a characteristic based method. Conserved scalar mean and variance transport equations were introduced to predict scalar mixing in reacting flows. Finally, a flarnelet thermochemistry model for turbulent non-premixed combustion with an assumed shape pdf for turbulence-chemistry interaction was incorporated. A method was identified whereby the temperature/ density provided by the combustion model was coupled directly back into the momentum equations rather than from the energy equation. Three different test cases were used to validate the numerical capabilities of the modified code, for isothermal and reacting flows on different grid types. The first case was the jet in confined cross flow associated with combustor liner-dilution jetcore flow interaction. The second was the swirling flow through a multi-stream swirler. These cases represent the main aerodynamic features of combustor primary zones. The third case was a methane-fueled coaxial jet combustor to assess the combustion model implementation. This study revealed that, via appropriate modifications, an unstructured density-based approach can be utilised to simulate combustor flows. It also demonstrated that unstructured meshes employing nonhexahedral elements were inefficient at accurate capture of flow processes in regions combining rapid mixing and strong convection at angles to cell edges. The final version of the algorithm demonstrated that low Mach RANS reacting flow simulations, commonly performed using a pressure-based approach, can successfully be reproduced using a density-based approach.

This dissertation describes detailed performance engineering and optimization of an unstructured computational aerodynamics software system with irregular memory accesses on various multi- and many-core emerging high performance computing scalable architectures, which are expected to be the building blocks of energy-austere exascale systems, and on which algorithmic- and architecture-oriented optimizations are essential for achieving worthy performance. We investigate several state-of-the-practice shared-memory optimization techniques applied to key kernels for the important problem class of unstructured meshes. We illustrate for a broad spectrum of emerging microprocessor architectures as representatives of the compute units in contemporary leading supercomputers, identifying and addressing performance challenges without compromising the floating-point numerics of the original code. While the linear algebraic kernels are bottlenecked by memory bandwidth for even modest numbers of hardware cores sharing a common address space, the edge-based loop kernels, which arise in the control volume discretization of the conservation law residuals and in the formation of the preconditioner for the Jacobian by finite-differencing the conservation law residuals, are compute-intensive and effectively exploit contemporary multi- and many-core processing hardware. We therefore employ low- and high-level algorithmic- and architecture-specific code optimizations and tuning in light of thread- and data-level parallelism, with a focus on strong thread scaling at the node-level. Our approaches are based upon novel multi-level hierarchical workload distribution mechanisms of data across different compute units (from the address space down to the registers) within every hardware core. We analyze the demonstrated aerodynamics application on specific computing architectures to develop certain performance metrics and models to bespeak the upper and lower bounds of the performance. We present significant full application speedup relative to the baseline code, on a succession of many-core processor architectures, i.e., Intel Xeon Phi Knights Corner (5.0x) and Knights Landing (2.9x). In addition, the performance of Knights Landing outperforms, at significantly lower power consumption, Intel Xeon Skylake with nearly twofold speedup. These optimizations are expected to be of value for many other unstructured mesh partial differential equation-based scientific applications as multi- and many- core architecture evolves.

The successful application of Computational Aeroacoustics (CAA) requires high accuracy numerical schemes with good dissipation and dispersion characteristics. Unstructured meshes have a greater geometrical flexibility than existing high order structured mesh methods. This work investigates the suitability of unstructured mesh techniques by computing a two-dimensionallinearised Euler problem with various discretisation schemes and different mesh types. The goal of the present work is the development of an unstructured numerical method with the high accuracy, low dissipation and low dispersion required to be an effective tool in the study of aeroacoustics. The suitability of the unstructured method is investigated using aeroacoustic test cases taken from CAA Benchmark Workshop proceedings. Comparisons are made with exact solutions and a high order structured method. The higher order structured method was based upon a standard central differencing spatial discretisation. For the unstructured method a vertex-based data structure is employed. A median-dual control volume is used for the finite volume approximation with the option of using a Green-Gauss gradient approximation technique or a Least Squares approximation. The temporal discretisation used for both the structured and unstructured numerical methods is an explicit Runge-Kutta method with local timestepping. For the unstructured method, the gradient approximation technique is used to compute gradients at each vertex, these are then used to reconstruct the fluxes at the control volume faces. The unstructured mesh types used to evaluate the numerical method include semi-structured and purely unstructured triangular meshes. The semi-structured meshes were created directly from the associated structured mesh. The purely unstructured meshes were created using a commercial paving algorithm. The Least Squares method has the potential to allow high order reconstruction. Results show that a Weighted Least gradient approximation gives better solutions than unweighted and Green-Gauss gradient computation. The solutions are of acceptable accuracy on these problems with the absolute error of the unstructured method approaching that of a high order structured solution on an equivalent mesh for specific aeroacoustic scenarios.

La simulation des phénomènes physiques exige souvent l’utilisation d’une discrétisation du milieu sous forme de maillage. Un exemple de ce type de situation est la simulation d’écoulement de fluides et la simulation du stress géomécanique pour les gisements pétroliers. Dans ces cas, le milieu étudié n’est pas homogène et l'hypothèse sur l’homogénéité de ce milieu peut mener à des résultats incorrects. C’est pourquoi la simulation des hétérogénéités est très importante pour ce genre de problèmes.Cette thèse est consacrée à la simulation géostatistique des hétérogénéités sur les maillages non-structurés par les méthodes géostatistiques non-linéaires. Le but de cette thèse est la création d’algorithmes de simulation des hétérogénéités directement sur les maillages non-structurés, sans utiliser les maillages fins réguliers intermédiaires et de l’upscaling. On présente deux modèles théoriques pour les simulations des variables continues sur les maillages non-structurés qui sont les deux versions différentes du modèle Gaussien discret (DGM) - DGM 1 et DGM 2. Le modèle théorique utilisé dans cette thèse permet de convertir le problème de simulation sur un maillage non-structuré en un problème de simulation d’un vecteur Gaussien multivarié et l’application de fonctions de transformation adaptées pour chaque élément du vecteur. La simulation de faciès est aussi envisagée en utilisant une généralisation des modèles pluri-Gaussiens et Gaussien tronqués pour les maillages non-structurés.L’application des méthodes développées est illustrée sur un gisement pétrolier - le cas d’étude X (gisement du gaz offshore). / Simulations of physical phenomenon often require discretizing the medium with a mesh. An example of this type of simulation is the simulation of fluid flow through a porous medium and the evaluation of the geomechanical stress in the petroleum reservoir. The studied medium is often not homogeneous and applying a homogeneity hypothesis can lead to incorrect simulation results. That makes simulation of heterogeneities important for this kind of problems.This thesis is devoted to geostatistical simulations of heterogeneities on unstructured grids using methods of non-linear geostatistics. The objective of this work is the development of algorithms for simulating heterogeneities directly on unstructured grids without using intermediate fine scale regular grids and upscaling. We present two theoretical models for geostatistical simulations of continuous parameters on unstructured grids which are different generalizations of the Discrete Gaussian model (DGM) – DGM 1 and DGM 2. The proposed theoretical models enable converting the problem of geostatistical simulation on an unstructured grid into the well-studied problem of simulating multivariate Gaussian random vectors followed by application of block-dependent transformation functions. The problem of simulating facies is also addressed in this work, for which generalizations of pluri-Gaussian and truncated Gaussian simulation models for unstructured grids are proposed.An application of the proposed methods is demonstrated on a case study X, which is an offshore gas reservoir with a tartan-meshed grid.

A computacao paralela, empregada no meio cientifico para resolucao de problemas que de- mandam grande poder computacional, teve nos ultimos anos o surgimento de um novo tipo de comunicacao entre instancias do paralelismo. Trata-se da Comunicacao Unilateral (CUL), onde somente uma instancia realiza a operacao de transferencia de informacoes, e esta ocorre em segundo plano, ao contrario da Comunicacao Bilateral (CBL), onde uma instancia envia a informacao e a outra recebe. Neste contexto se buscou analisar os beneficios que a CUL agrega ao paralelismo de um programa que se utiliza de uma grade nao estruturada em me- moria. Duas formas de apoio ao paralelismo foram utilizadas: uma biblioteca, a \"Message Passing Interface\" (MPI) (especificamente a sua parte que descreve a CUL), e uma extensao a linguagem Fortran, o Coarray Fortran (CAF). A semantica do MPI CUL e mais complexa que a do CAF, mas a do CAF e mais restritiva. Para analisar a semantica e desempenho da CUL foi realizada uma ambientacao utilizando MPI CUL e CAF no paralelismo de um programa simples, denominado jogo da Vida (Game of Life), com grade estruturada e com otimo desempenho paralelo atraves do MPI CBL. Na programacao o MPI CUL se mostrou verborragico (aumento do numero de linhas de codigo) e complexo, principalmente quando se utiliza um controle refinado de sincronismo entre as imagens. Ja o CAF reduziu o nu- mero de linhas de codigo (entre 20% e 40%), e o sincronismo e muito mais simples. Os resultados mostraram uma piora no desempenho no caso do MPI CUL, mas para o CAF o desempenho absoluto foi melhor que a implementacao original ate o numero de nucleos de processamento que compartilham a mesma memoria. Para grades nao estruturadas se utilizou o Ocean Land Atmospheric Model (OLAM), um modelo de simulacao do sistema terrestre com grade baseada em prismas triangulares, paralelizado atraves de MPI CBL. A implementacao da comunicacao por MPI CUL na estrutura do paralelismo existente mos- trou que esta semantica possui alguns pontos que podem prejudicar a programacao, como o tratamento da exposicao de memoria (cada instancia tem uma memoria exposta de tamanho diferente) e como e realizado o sincronismo entre as instancias. Em termos de desempenho as curvas de speed-ups mostraram que o MPI CUL prejudicou o OLAM independentemente da implementacao das bibliotecas ou do equipamento utilizado, com reducao de pelo menos 20% no speed-up para sete ou mais processadores. Assim como no jogo da Vida o MPI com comunicacao unilateral penalizou o desempenho. / Parallel computing is used to solve many scientific problems that demand intensive compu- ting power. Recently a new paradigm of communication between instances of the parallelism has appeared, called the one-sided communication (OSC), where only one instance performs the operation of information transfer, occurring in the background, as opposed to the two- sided communication (TSC), where one instance sends the information and the other receives it. In this context we analyze the benefits that OSC aggregates to the parallelism of a pro- gram that uses an unstructured grid in memory. Two OSC implementations were used: the \"Message Passing Interface\" (MPI) library (specifically the part that describes OSC), and Coarray Fortran (CAF), an extension of the Fortran language. The semantics of MPI OSC is more complex than that of CAF, but the semantics of CAF is more restrictive. To analyze the semantics and performance of OSC a simple program called Game of Life is used in a structured grid, giving very good parallel performance through MPI TSC. The MPI OSC program was verbose (increase in the number of lines of code) and complex, especially when using a more refined control to synchronize the parallel instances. On the other hand, CAF has reduced the number of lines of code (between 20% to 40%), and the synchronization is very simple. The results showed a worse performance in the case of MPI OSC, but for the CAF the absolute performance was better than the original implementation up to the number of processor cores that share the same memory. For unstructured grids we used the Ocean Land Atmospheric Model (OLAM), an earth simulation model on a grid based on triangular prisms, and parallelized with MPI TSC. The implementation with MPI OSC showed that this semantics has some points that may affect the coding of the communication structure, as in the treatment of memory exposure (each instance has an exposed memory of different size) and the way to treat the synchronization among instances. In terms of performance, the speedup curves showed that MPI OSC penalized OLAM, independently of the MPI implementation or the equipment used, with a reduction of at least 20% in speedup for seven or more processors. As in the Game of Life, MPI OSC degrades the performance.

The results from computer simulations of the gas-dynamic processes that occur during and after the rupture of diaphragms within shock tubes and expansion tubes are presented. A two-dimensional and axisymmetric finite-volume code that solves the unsteady Euler equations for inviscid compressible flow, was used to perform the simulations. The flow domains were represented as unstructured meshes of triangular cells and solution-adaptive remeshing was used to focus computational effort in regions where the flow-field gradients were high. The ability of the code to produce accurate solutions to the Euler equations was verified by examining the following test cases: supersonic vortex flow between two arcs, an ideal shock tube, and supersonic flow over a cone. The ideal shock tube problem was studied in detail, in particular the shock speed. The computed shock speed was accurate when the initial pressure ratio was low. When the initial pressure ratio was high the ow was dificult to resolve because of the large density ratio at the contact surface where significant numerical diffusion occurred. However, solution- adaptive remeshing was used to control the error and reasonable estimates for the shock speed were obtained. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm within a shock tube. The development of the flow, in particular the contact surface was examined and found to be strongly dependent on the initial pressure ratio across the diaphragm. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one- dimensional models. The shock speeds computed via the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and were closer to the experimental measurements. This indicates that multi- dimensional ow effects were partly responsible for the relatively high shock speeds measured in the experiments. The code also has the ability to simulate two-dimensional fluid-structure interac- tions. To achieve this the Euler equations are solved for a general moving frame of reference. Mesh management during a simulation is important. This includes the ability to automatically generate a new mesh when the current mesh becomes distorted (due to the motion of the structures) and the transfer of the solution from the old mesh to the new. The shock induced rupture of thin diaphragms was examined. Previous one dimen- sional models are awed because they do not simultaneously consider the diaphragm mass and allow the upstream gas to penetrate the diaphragm mass. Two multi- dimensional models which allow the upstream gas to penetrate are described. The first model assumes the diaphragm vaporises immediately after the arrival of the incident shock. The second model assumes the diaphragm shatters into a number of pieces which can be treated as rigid bodies. The results from both models are compared with experimental data.

A computacao paralela, empregada no meio cientifico para resolucao de problemas que de- mandam grande poder computacional, teve nos ultimos anos o surgimento de um novo tipo de comunicacao entre instancias do paralelismo. Trata-se da Comunicacao Unilateral (CUL), onde somente uma instancia realiza a operacao de transferencia de informacoes, e esta ocorre em segundo plano, ao contrario da Comunicacao Bilateral (CBL), onde uma instancia envia a informacao e a outra recebe. Neste contexto se buscou analisar os beneficios que a CUL agrega ao paralelismo de um programa que se utiliza de uma grade nao estruturada em me- moria. Duas formas de apoio ao paralelismo foram utilizadas: uma biblioteca, a \"Message Passing Interface\" (MPI) (especificamente a sua parte que descreve a CUL), e uma extensao a linguagem Fortran, o Coarray Fortran (CAF). A semantica do MPI CUL e mais complexa que a do CAF, mas a do CAF e mais restritiva. Para analisar a semantica e desempenho da CUL foi realizada uma ambientacao utilizando MPI CUL e CAF no paralelismo de um programa simples, denominado jogo da Vida (Game of Life), com grade estruturada e com otimo desempenho paralelo atraves do MPI CBL. Na programacao o MPI CUL se mostrou verborragico (aumento do numero de linhas de codigo) e complexo, principalmente quando se utiliza um controle refinado de sincronismo entre as imagens. Ja o CAF reduziu o nu- mero de linhas de codigo (entre 20% e 40%), e o sincronismo e muito mais simples. Os resultados mostraram uma piora no desempenho no caso do MPI CUL, mas para o CAF o desempenho absoluto foi melhor que a implementacao original ate o numero de nucleos de processamento que compartilham a mesma memoria. Para grades nao estruturadas se utilizou o Ocean Land Atmospheric Model (OLAM), um modelo de simulacao do sistema terrestre com grade baseada em prismas triangulares, paralelizado atraves de MPI CBL. A implementacao da comunicacao por MPI CUL na estrutura do paralelismo existente mos- trou que esta semantica possui alguns pontos que podem prejudicar a programacao, como o tratamento da exposicao de memoria (cada instancia tem uma memoria exposta de tamanho diferente) e como e realizado o sincronismo entre as instancias. Em termos de desempenho as curvas de speed-ups mostraram que o MPI CUL prejudicou o OLAM independentemente da implementacao das bibliotecas ou do equipamento utilizado, com reducao de pelo menos 20% no speed-up para sete ou mais processadores. Assim como no jogo da Vida o MPI com comunicacao unilateral penalizou o desempenho. / Parallel computing is used to solve many scientific problems that demand intensive compu- ting power. Recently a new paradigm of communication between instances of the parallelism has appeared, called the one-sided communication (OSC), where only one instance performs the operation of information transfer, occurring in the background, as opposed to the two- sided communication (TSC), where one instance sends the information and the other receives it. In this context we analyze the benefits that OSC aggregates to the parallelism of a pro- gram that uses an unstructured grid in memory. Two OSC implementations were used: the \"Message Passing Interface\" (MPI) library (specifically the part that describes OSC), and Coarray Fortran (CAF), an extension of the Fortran language. The semantics of MPI OSC is more complex than that of CAF, but the semantics of CAF is more restrictive. To analyze the semantics and performance of OSC a simple program called Game of Life is used in a structured grid, giving very good parallel performance through MPI TSC. The MPI OSC program was verbose (increase in the number of lines of code) and complex, especially when using a more refined control to synchronize the parallel instances. On the other hand, CAF has reduced the number of lines of code (between 20% to 40%), and the synchronization is very simple. The results showed a worse performance in the case of MPI OSC, but for the CAF the absolute performance was better than the original implementation up to the number of processor cores that share the same memory. For unstructured grids we used the Ocean Land Atmospheric Model (OLAM), an earth simulation model on a grid based on triangular prisms, and parallelized with MPI TSC. The implementation with MPI OSC showed that this semantics has some points that may affect the coding of the communication structure, as in the treatment of memory exposure (each instance has an exposed memory of different size) and the way to treat the synchronization among instances. In terms of performance, the speedup curves showed that MPI OSC penalized OLAM, independently of the MPI implementation or the equipment used, with a reduction of at least 20% in speedup for seven or more processors. As in the Game of Life, MPI OSC degrades the performance.

No description available.

Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder. / Master of Science / Coarse Grid Projection (CGP) methodology is a new multigrid technique applicable to pressure projection methods for solving the incompressible Navier-Stokes equations. In the CGP approach, the nonlinear momentum equation is evolved on a fine grid, and the linear pressure Poisson equation is solved on a corresponding coarsened grid. Mapping operators transfer the data between the grids. Hence, one can save a considerable amount of CPU time due to reducing the resolution of the pressure filed while maintaining excellent to reasonable accuracy, depending on the level of coarsening.

A set of algorithms building a program package for the generation of twoandthree-dimensional unstructured/hybrid grids around complex geometrieshas been developed. The unstructured part of the grid generator is based on the advancing frontalgorithm. Tetrahedra of variable size, as well as directionally stretched tetrahedracan be generated by specification of a proper background grid, initiallygenerated by a Delaunay algorithm. A marching layer prismatic grid generation algorithm has been developedfor the generation of grids for viscous flows. The algorithm is able to handleregions of narrow gaps, as well as concave regions. The body surface is describedby a triangular unstructured surface grid. The subsequent grid layers in theprismatic grid are marched away from the body by an algebraic procedurecombined with an optimization procedure, resulting in a semi-structured gridof prismatic cells. Adaptive computations using remeshing have been done with use of a gradientsensor. Several key-variables can be monitored simultaneously. The sensorindicates that only the key-variables with the largest gradients give a substantialcontribution to the sensor. The sensor gives directionally stretched grids. An algorithm for the surface definition of curved surfaces using a biharmonicequation has been developed. This representation of the surface canbe used both for projection of the new surface nodes in h-refinement, and theinitial generation of the surface grid. For unsteady flows an algorithm has been developed for the deformationof hybrid grids, based on the solution of the biharmonic equation for the deformationfield. The main advantage of the grid deformation algorithm is that itcan handle large deformations. It also produces a smooth deformation distributionfor cells which are very skewed or stretched. This is necessary in orderto handle the very thin cells in the prismatic layers. The algorithms have been applied to complex three-dimensional geometries,and the influence of the grid quality on the accuracy for a finite volumeflow solver has been studied for some simpler generic geometries. / QC 20100812